iMac shut down and reboot issue

You can save you and us a lot of time and effort if you do the following:

Please navigate to the Mac App Store or navigate to www.Etrecheck.com and download the free version of EtreCheck. Once you have you downloaded the app and installed it, please run the report and save it. This report will help us get a good idea what has been installed on your system and help us be able to diagnose what may be wrong.

When you have your report, you can attach it when you reply to this message and we can then review it and help you determine what is needed to get your system running well again. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message please click https://discussions.apple.com/docs/DOC-250000211

Looking at what has been installed I see a lot of old and frankly garbage ware installed. I suspect you have multiple outdated applications installed that are not designed for the version of Mac OS installed. What you need to do with those is to inventory your third party apps and ensure you are running the most up-to-date versions that are designed for the version of Mac OS installed. If the vendors do not have versions for the version of Mac OS currently installed, those apps should be uninstalled. Then empty the Trash.

I also see you have a 5+ years old Fusion drive installed. I would recommend that you restart in the Recovery Partition (hold down Command + R on startup) and open Disk Utility. Then run First Aid at least 3-4 times and look for errors, if you see any then your HD is failing and should be replaced. In that case I'd recommend installing a SSD to replace the spinning HD.

Finally, you also may have a failing external peripheral that is causing the problem. The only way to troubleshoot these is to remove all wired peripherals (printers, external HDs, etc..) and then run the computer. If the failures go away, then you know it is one of your peripherals. To find which one you need to add them back 1 by 1 and then test until you find the one causing the problem.

The instructions to attach the scans are in my original post.